Quantum Fisher Information as a Probe of Sterile Neutrino New Physics:Geometric Advantage of KM3NeT over IceCube

Abstract

We investigate a reported discrepancy between a high-energy neutrino detection at KM3NeT and its non-observation at IceCube, which suggests a statistical tension of up to 3.5 standard deviations. This gap has been proposed to arise from sterile neutrino oscillations over the 147-kilometer path to KM3NeT, driven by either matter-induced resonances or nonstandard interactions. Using the Quantum Fisher Information framework, we quantify the sensitivity of the neutrino state to these new physics couplings and establish fundamental precision limits via the quantum Cramer-Rao bound. Our analysis shows that the information available at KM3NeT exceeds that at IceCube by three orders of magnitude for matter-induced scenarios. We demonstrate that IceCube would require over thirty times more events to match the precision of a single KM3NeT detection. We identify an optimal baseline of 150 to 200 kilometers, placing KM3NeT in a superior position for these measurements. Our results show that standard detection methods already reach the ultimate quantum precision limit, and that a small number of future events at KM3NeT could provide the first quantum-limited constraints on sterile neutrino couplings.

Figures (8)

• Figure 1: Quantum Fisher Information $F_Q(\in_{ss})$ (solid) and conversion probability $P_{s\mu}$ (dotted) as functions of baseline $L$, evaluated at $\in_{ss} = 225$, $m_s = 3~{\rm keV}$, $\theta = 10^{-2}$, $E_\nu = 220~{\rm PeV}$. Top: KM3NeT. Bottom: IceCube. Vertical dashed lines mark the actual detector baselines. Dips in $F_Q$ correspond to oscillation nodes where $P_{s\mu} \to 0$, at which the experiment is blind to $\in_{ss}$ regardless of statistics.
• Figure 2: Quantum Cramér-Rao bound $\Delta_{\rm CRB}(\in_{ss})$ as a function of baseline $L$ for KM3NeT (top) and IceCube (bottom), for $N=1$ event. At the KM3NeT baseline (dashed), $\Delta_{\rm CRB} \sim \mathcal{O}(12.7)$; at IceCube, $\Delta_{\rm CRB} \sim \mathcal{O}(419)$.
• Figure 3: Quantum Fisher Information $F_Q(m_s)$ (solid) and conversion probability $P_{s\mu}$ (dotted) as functions of baseline $L$, at $\varepsilon_{ss} = 225$, $m_s = 3~{\rm keV}$. The absolute values of $F_Q(m_s)$ are smaller than $F_Q(\in_{ss})$ by several orders of magnitude, reflecting the weaker mass sensitivity at fixed energy and baseline.
• Figure 4: Quantum Cramér-Rao bound $\Delta_{\rm CRB}(m_s)$ in units of $m_s$ as a function of baseline $L$ for KM3NeT (top) and IceCube (bottom). The minimum of $\Delta_{\rm CRB}(m_s)$ near the first oscillation maximum provides the tightest mass constraint. At the KM3NeT baseline, $\Delta_{\rm CRB}(m_s) \sim \mathcal{O}(10^2)$--$\mathcal{O}(10^3)$.
• Figure 5: Quantum Fisher Information $F_Q(\varepsilon_{\mu s})$ (solid) and conversion probability $P_{s\mu}$ (dotted) as functions of baseline $L$, evaluated at $\in_{\mu s} = 1$, $m_s = 500~{\rm eV}$, $\theta = 10^{-4}$, $E_\nu = 220~{\rm PeV}$. Top: KM3NeT. Bottom: IceCube. Vertical dashed lines mark the actual detector baselines.